Evaluate
\frac{119}{33}\approx 3.606060606
Factor
\frac{7 \cdot 17}{3 \cdot 11} = 3\frac{20}{33} = 3.606060606060606
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)119}\\\end{array}
Use the 1^{st} digit 1 from dividend 119
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)119}\\\end{array}
Since 1 is less than 33, use the next digit 1 from dividend 119 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)119}\\\end{array}
Use the 2^{nd} digit 1 from dividend 119
\begin{array}{l}\phantom{33)}00\phantom{4}\\33\overline{)119}\\\end{array}
Since 11 is less than 33, use the next digit 9 from dividend 119 and add 0 to the quotient
\begin{array}{l}\phantom{33)}00\phantom{5}\\33\overline{)119}\\\end{array}
Use the 3^{rd} digit 9 from dividend 119
\begin{array}{l}\phantom{33)}003\phantom{6}\\33\overline{)119}\\\phantom{33)}\underline{\phantom{9}99\phantom{}}\\\phantom{33)9}20\\\end{array}
Find closest multiple of 33 to 119. We see that 3 \times 33 = 99 is the nearest. Now subtract 99 from 119 to get reminder 20. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }20
Since 20 is less than 33, stop the division. The reminder is 20. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}